At the bottom of this post is the description for resort refillable mugs in the Disney website menu for Contempo Cafe. Our last few trips we've purchased mugs at our hotel, tossed them in our backpack, and used them whenever we've left a park for a meal at a nearby resort quick service (for example, on MK days we sometimes hop on the monorail and have lunch at Gasparilla at Grand Floridian). Regardless of the number of nights you've booked, the cup is usually programmed to work for 2-3 weeks, and I'm guessing that if you were staying longer you could have it extended.
"Eligible for refills at Beverage Islands at Quick-service locations at any Disney Resort Hotel during the length of your stay"